In this paper, the free vibration of conical panels is analyzed by the mesh-free kp-Ritz method. Both 1-D and 2-D versions of the kp-Ritz approach are formulated for conical panels. For conical panels with two simply supported straight edges, the 1-D kp-Ritz version is used, where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2-D displacement field. For conical panels having arbitrary boundary conditions, the displacement field is approximated by the 2-D kp-Ritz version, with 2-D form of kernel particle functions employed. The classical thin shell theory based on Love's hypothesis is employed in the present analyses, and based on the kernel particle concept and Ritz technique, the eigenequations of the frequencies of the conical panels are obtained. To validate the accuracy of stability of the present method, convergence studies were carried out based on the influences of the support size and the number of nodes. Comparisons were also made with existing results available in the open literature. This study also examines in detail the effects of variation in the semi-vertex angle and boundary conditions, on the frequency characteristics of conical panels.